Virtual colonoscopy is a non-invasive screening procedure aimed at exploring the inner colonic surface, typically in a search for lesions. Standard methods in virtual colonoscopy generally try to simulate conventional colonoscopy techniques by using “virtual fly-throughs” of the reconstructed colon image. Major problems associated with such techniques include the time required to navigate through the complex colon shape and the number of areas that are often inadvertently left uninspected as they remain occluded behind Haustral folds. A number of techniques have been proposed to alleviate these problems, including utilizing Mercator projections (see, for example, Paik, D., Beaulieu, C, Jeffrey, R. C. A., Karadi, C, S., Napel, S., “Visualization modes for CT colonography using Cylindrical and planar map projections”, J. Comput Assist. Tomogr. vol. 24(2), pp. 179-188 (2000)); an unfolded cube display (see, for example, Vos, F., Serlie, I., van Gelder, R., Post, F. Truyen, R., Gerritsen, F., Stoker, J., Vossepoel, A., A New Visualization Method for Virtual Colonoscopy, MICCAI 2001: 645-654, (2001)); and panoramic projections (see, for example, Geiger, B., Chefd'hotel, C, Sudarsky, S., Panoramic Views for Virtual Endoscopy, Duncan, J, Gerig, G. (eds), MICCAI 2005, LNCS 3749, 662-669, Springer-Verlag, (2005)).
Recently, an alternative approach has emerged in the literature which proposes the use of virtual dissection of the colonic surface to speed up the inspection process. With this technique, the 3D model of the colon is cut open longitudinally and displayed as a single flat image. This approach has the potential of decreasing the inspection time and at the same time reducing the number of blind areas. However, it is well known that the colon lumen cannot be flattened onto a plane without introducing some deformations. See Johnson K., Johnson C., Fletcher, J., MacCarty, R., Summers, R., CT colonography using 360-degree virtual dissection: a feasibility study. AJR Am J Roentgenol; 186:90-95, (2006).
A number of methods have been proposed to digitally straighten and unfold the colon to expose the entire colon lumen as a single image. A uniform sampling technique using planar cross sections orthogonal to the centerline is proposed in Wang, G, Vannier, M., Unraveling the GI tract by spiral CT, SPIE 1995, 307-315. (1995).
The results appear to be acceptable for portions of the colon that are fairly linear, but produce undesirable results in high curvature areas. This straightforward sampling can lead to single lesions being displayed more than once or missed completely. To overcome these limitations, a method has been proposed for transforming the colon into a straight cylinder-like shape based on the characteristics of the electrical field of a charged centerline. See Wang. G. McFarland. E., Brown, B. Vannier, M., GI tract unraveling with curved cross sections; IEEE Transactions on Medical Imaging, vol. 17, no. 2, April 1998, hereby incorporated herein by reference.
When the entire centerline is charged, the curved cross-sectional planes generated tend to diverge, thereby avoiding the double sampling problem. However, since the method is so computationally expensive, the path is changed only locally and therefore there is no guarantee that the cross sections will not intersect. The method is computational expensive requiring in the order of 6 hours of computational time, according to Zhang in the paper cited below, by X. Zhang and J. Yang.
A method to map the entire colon surface onto a flat surface using a conformal mapping is proposed in Haker, S., Angenent, S., Tannenbaum, A., Kikinis, R., “Nondistorting Flattening for Virtual Colonoscopy”, Proc. MICCAI 2000, 358-366, (2000). It is based on a discretization of the Laplace-Beltrami operator for flattening a surface onto a plane in a manner that preserves local geometry. The flattened surface is then color-coded based on the mean curvature.
Bartroli et al. propose a new approach to deal with the problems of double appearance of lesions and non-uniform sampling. Their technique works by casting rays that follow the negative gradient direction of a distance map generated from the centerline. These rays are curved and do not intersect. The distance between the ray origins and the hit surface point determine a height field. The height field is then unfolded and a non linear scaling is applied to compensate for distortions introduced by the non uniform sampling. The computational time for the entire process is in the range of hours. See Bartroli, A. Wegenkittl, R. König, A., Gröller, E., “NonLinear Virtual Colon Unfolding”. Proc. IEEE Visualization, 411:420 (2001), hereby incorporated herein by reference.
Silver et al. propose an algorithm to manipulate volumetric datasets using volumetric skeletons. The authors use the term skeleton to refer to a thinned volume that retains the essential shape of the original volume and it is computed using a reversible thinning procedure based on a distance transform. The skeleton can be interactively manipulated and the deformed volume reconstructed via an inverse transformation. See Silver, D. Gagvani, N. Unwinding the Colon, Medicine Meets Virtual Reality (MMVR) 2002, hereby incorporated herein by reference.
In the work of Zhang et al., the colon straightening is modeled as a solid elastic deformation process with special constraints and boundary conditions. The deformation model is described by a group of partial differential equations based on equilibrium and kinematic equations found in solid mechanics theory. See Zhang, Z., Ackerman M., Li, J. “Colon straightening based on an elastic mechanics model”, ISBF04, IEEE, 292-295, (2004).
Hong et al. present an algorithm that flattens the colon in a conformal manner and minimizes the global distortion. The conformal parameterization is solved using finite element methods to approximate a solution of an elliptic partial differential equation on surfaces. The entire process takes about 30 minutes for a 512×512×460 data set. See Hong, W., Gu. X., Qiu, F., Jin, M., Kaufman. A, “Conformal Virtual Colon Flattening”, SPM 2006, Cardiff Wales. 85-93 (2006).
Also of interest in this context are Lim, S. Lee, H., Shin B. “Surface Reconstruction for Efficient Colon Unfolding”, Kim M. Shimada, K., (eds.). GMP 2006. LNCS 4077. 623-629. Springer-Verlarg (2006); and Gibson, S., Calculating the Distance Map for Binary Sampled Data, Technical Report TR99-26, Mitsubishi, 1999